#1, I don't know where you are getting the idea that something that is insulting to a protected racial group is unprotected as "fighting words." That simply isn't true.
#2 RE: the highlighted: The fact that a form of speech could be interpreted one way is not sufficient to cause it to be unprotected.
I don't believe that a court has ever decided that insulting depictions of minorities on public land are not protected as free speech, but I am not certain it is as clear cut as you state. There are definite rules against displaying
inside places of work and public buildings images that create a hostile work space or seek to discourage certain customers from patronizing the establishment. And being able to interpret the same image in an unoffensive manner does not automatically allow it to be displayed. Displaying gratuitous images of naked women in sexual posses in an office is considered creating a hostile work space even if some might see them as "art." The general rule is how a "reasonable person" would react.
IANAL, but I can imagine someone arguing that the rules apply outside on publicly held land. I suspect it might be a hard sell, but not because of the "free speech" issue: I doubt that a statue
on public land that depicted a Nazi stereotype of a Jew with a large nose, bags of money, and leering over a "white" woman, or a KKK stereotype of a Black person, would survive its first court test. Rather in the case of Civil War monuments the court would have to be convinced that the imagery was so inherently offensive as to offend a "reasonable person." Undoubtedly it would depend on the monument. Again IANAL, but I at least I know that I am not. I am speculating but I do think that the issue is more complex than you think.
More generally, and relating to morality rather than to law: I see public space as being owned by all the public and find it very questionable to have on display statues that are offensive to a large percent of the public. I am not suggesting that people have a right not to be offended: all types of speech, images, etc. should be allowed in public spaces, no matter how offensive,
as long as these are expressions of private individuals or groups. But it is a different matter for certain speech, images, statues
to be endorsed by the government. Although typically erected by private groups, most of the Confederate monuments are clearly endorsed by government- they are allowed to remain on public land unlike other art, and are generally maintained and protected by the government. Further, I suspect that erecting a Civil War monument in Georgia dedicated to General Sherman would run into serious problems, indicating that one point of view is being officially endorsed versus to another.